Closest Pair

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Line Sweep Algorithm

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Divide and Conquer

The problem can be solved in O(n log n) time using the recursive divide and conquer approach, e.g., as follows[1]:

  1. Sort points along the x-coordinate
  2. Split the set of points into two equal-sized subsets by a vertical line
  3. Solve the problem recursively in the left and right subsets. This will give the left-side and right-side minimal distances.
  4. Find the minimal distance among the pair of points in which one point lies on the left of the dividing vertical and the second point lies to the right.
  5. The final answer is the minimum among the left, middle, and right deltas.

Originally taken from:

Example Problems

UVa 10245

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